Question: Nadia is 8 years older than Emily. Twenty years ago, Nadia was 3 times as old as Emily. How old is Emily now?
Answer: We can use the given information to write down two equations that describe the ages of Nadia and Emily. Let Nadia's current age be $n$ and Emily's current age be $e$ The information in the first sentence can be expressed in the following equation: $n = e + 8$ Twenty years ago, Nadia was $n - 20$ years old, and Emily was $e - 20$ years old. The information in the second sentence can be expressed in the following equation: $n - 20 = 3(e - 20)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $e$ , it might be easiest to use our first equation for $n$ and substitute it into our second equation. Our first equation is: $n = e + 8$ . Substituting this into our second equation, we get the equation: $(e + 8)$ $-$ $20 = 3(e - 20)$ which combines the information about $e$ from both of our original equations. Simplifying both sides of this equation, we get: $e - 12 = 3 e - 60$ Solving for $e$ , we get: $2 e = 48$ $e = 24$.